Grade VI Mathematics Topic: Understanding Symmetry and Creating Symmetry and Patterns Duration: 6–7 periods (40–45 minutes each) Suitable for CBSE / ICSE / State Boards / Common Core
Learning Objectives
By the end of this unit students will be able to:
- Identify, draw and count lines of symmetry in regular and irregular 2D shapes (up to 10 lines)
- Determine the order and angle of rotational symmetry of any 2D shape
- Differentiate between line symmetry, rotational symmetry and asymmetry
- Recognise and create repeating and growing patterns in numbers and shapes
- Complete reflections and rotations of shapes on grid paper
- Find examples of symmetry in nature, architecture, art and daily objects
- Create original symmetrical artwork using paper folding and mirror reflection
Key Vocabulary
Line of symmetry, mirror line, reflection, rotational symmetry, order of rotation, centre of rotation, angle of rotation, repeating pattern, growing pattern, tessellation, symmetric, asymmetric, radial symmetry
Complete List of Teaching Materials Required
- Whiteboard, markers, duster
- Geometry box for every student (ruler, protractor, compass, set squares)
- A4 plain sheets, A4 coloured sheets, square dot-grid sheets (10×10)
- Scissors, glue stick, transparent tape
- Small hand mirrors or Mira (at least one per pair)
- Transparent OHP sheets or tracing paper (for rotation demo)
- Printed shape cards (regular polygons from triangle to decagon, English capital letters, arrows, hearts, stars, etc.)
- Real objects or high-quality pictures: butterfly, leaf, starfish, feather, snowflake, flower, honeycomb, Taj Mahal, Islamic tile work, rangoli/kolam designs, kaleidoscope images
- Laptop + projector (optional) for showing GeoGebra symmetry applets
- Chart paper and sketch pens for gallery walk
Detailed Day-wise Lesson Plan (without columns)
Period 1 – Introduction to Line Symmetry Start with a “What do you notice?” activity. Show a butterfly, human face, Taj Mahal photo and ask, “If I draw a line down the middle, do both sides match?” Students fold square, rectangle, equilateral triangle and circle papers to discover lines of symmetry themselves. Introduce the term “line of symmetry” or “mirror line”. Quick game: Teacher holds up shape cards, students shout the number of lines of symmetry.
Period 2 – Lines of Symmetry in Regular and Irregular Shapes Distribute printed shape cards. Students work in pairs to draw every possible line of symmetry with pencil and then trace with red sketch pen. Fill a common class table on the board: Equilateral triangle → 3, Square → 4, Regular pentagon → 5 … Circle → infinite lines. Discuss irregular shapes (scalene triangle → 0, isosceles → 1, kite → 1, arrow → 1, letter “A” → 1, letter “B” → 0). Memory tip: “A regular polygon with n sides has exactly n lines of symmetry.”
Period 3 – Rotational Symmetry Demonstrate with a transparent square: rotate 90°, 180°, 270°, 360° and ask when it looks exactly the same. Define: “The order of rotational symmetry is the number of times a shape looks exactly the same in one full 360° turn.” Angle of rotation = 360° ÷ order. Students test equilateral triangle (order 3), square (order 4), regular hexagon (order 6), swastik (order 4), letter “S” (order 2), letter “Z” (order 2), parallelogram (order 2).
Period 4 – Hands-on Paper Folding and Mirror Play Ink-blot butterflies: drop paint on one half, fold, press → open for perfect symmetry. Paper snowflakes: fold circle multiple times and cut small patterns. Mirror activity: give half-drawn shapes with the mirror line marked; students place mirror on the line and draw the missing half. Create a simple rangoli or kolam using only folding and single cut.
Period 5 – Patterns and Tessellation Number patterns: find the rule and next three terms Example 1: 3, 7, 11, 15, … (add 4 each time) Example 2: 2, 6, 18, 54, … (multiply by 3) Example 3: 1, 4, 9, 16, 25, … (square numbers)
Shape patterns: create a border design using reflection and rotation of one motif (e.g., rotate a fish 90° four times to make a repeating pattern). Show how only triangles, squares and hexagons tessellate with regular polygons. Students colour a small tessellation.
Period 6 – Symmetry in Nature, Art and Culture (Gallery Walk) Display 15–20 pictures around the classroom: flowers (5 or 6 petals), starfish, honeycombs, Roman mosaics, Islamic geometric patterns, Warli painting, mandala, kaleidoscope. Each group gets one picture, prepares a 2-minute explanation of line and rotational symmetry in it, and presents. Conclude with a discussion: “Symmetry makes things beautiful and balanced.”
Period 7 (Optional) – Assessment and Fun Challenge 30–40 mark written test + hands-on task (create a symmetrical greeting card).
Ready-to-Print Worksheets and Assessment (all included)
- Lines of Symmetry Table (fill in the blanks)
- Rotational Symmetry – write order and smallest angle for 10 shapes/letters
- Complete the shape by reflection (6 half-shapes given)
- Rotate the shape 90°, 180° on dot grid (4 questions)
- Find the next three terms and write the rule (6 number patterns)
- Draw a repeating border pattern using rotation of one shape
- Multiple choice + match the following (10 questions)
- Creative task: Design a symmetrical logo for your school using at least 4 lines of symmetry